Algebra word problem

Question

Sarah started school at the age of five. She spent one quarter of her life being educated, and went straight to work. After working for one half of her life, she lived for fourteen happy years after retirin. How old was she when she retired?

Answer 1

Define the variable:

Let r = retirement age

Given : 5 yo when she started school 

Death = r + 14

Working:  1/2(r + 14)

Education: 1/4(r + 14)

 

Set the equation up in the way that makes sense:

5 years + work + education + 14 years = total lifetime

5 + 1/2(r+14) + 1/4(r+14) + 14 = r + 14

5 + 1/2r + 7 + 1/4r + 7/2 = r 

12 + 7/2 + 3/4r = r

31/2 = 1/4r

r = 62

 

Sarah was 62 years old when she retired.

Sarah spent 38 years working.

Sarah spent 19 years being educated.

Sarah was 76 years old when she died.

Answer 2

Peyton,

 

Assume Sarah lived for x years

 

She spent qtr. life on education so that is x/4 yrs

 

She worked for 1/2 her life = x/2 yrs

 

She lived 14 yrs after retiring

 

Also. she was 5 when she started school

 

Adding all up

 

5 + x/4 + x/2 + 14 = x

19 + 3/4x = x

1/4x = 19

x = 76

 

To calculate how old she was when she retired, subtract 14 from the life

 

76 - 14 = 62

 

She was 62 at retirement